Abstract
Using the measure-transformation approach, an exact, computable optimal filter for a particular class of nonlinear filtering problems in discrete time is derived. This filter is also used to approximate the optimal filter for a large class of discrete-time filtering problems arising in applications. Convergence of the approximations is proved and bounds on the quality of the approximations derived.
Work partially supported by the Consiglio Nazionale delle Ricerche (C.N.R.) under contract N.80.02343.01.
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References
G.B. Di Masi and W.J. Runggaldier, "Continuous-time approximations for the nonlinear filtering problem", Appl. Math. and Opt. 7, 233–245, 1981.
G.B. Di Masi and W.J. Runggaldier, "On measure transformations for combined filtering and parameter estimation in discrete time", Systems & Control Letters 2, 57–62, 1982.
H.J. Kushner, "Probability methods for approximations in stochastic control and for elliptic equations", Academic Press 1977.
E. Wong, "Stochastic Processes in Information and Dynamical Systems", McGraw-Hill 1971.
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© 1982 Springer-Verlag
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Di Masi, G.B., Runggaldier, W.J. (1982). Approximations and bounds for discrete-time nonlinear filtering. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044391
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DOI: https://doi.org/10.1007/BFb0044391
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